(I know it sounds like a really terrible problem.)
I've let LE play with sippy cups for a few months, but they all have the most ridiculous anti-spill mechanisms. One she needs to bite the spout and then suck - not a trick that a nursing mother wants her child with 3 teeth to learn! Another has a straw and you have to suck with all your might to get anything out. I'm sure there are better options out there, but these are the two we have.
I saw a mommy friend offering her nalgene bottle with a flexible straw inside to her toddler and thought that was a pretty brilliant, yet simple idea. She said you can teach baby's to suck by starting with a smoothie via straw - this gives them incentive to learn how to make the straw work. So, today I made LE a basic smoothie (plain whole milk yogurt with some frozen strawberries and peaches) and SHE LEARNED TO USE A STRAW instantly! I was so proud of my baby.
(I promise she doesn't wear this dress everyday...it just keeps making it in photos.)